# Anthony vs. Carmelo

## Introduction

Carmelo and Anthony are both good friends, although they are having a dispute over whose rent deal is better. Anthony currently lives in a basement and Carmelo lives in an apartment. Their rental areas are both the same distance from the university which they attend but they both want to save money and see which rental area will be to their advantage in the long run.

Both of their rents are based on a monthly scale and a fee is given every month to the renter or owner. The only difference between each payment is that Anthony has an initial fee and then a monthly fee ,but Carmelo has a monthly fee.

## How do we solve this?

In order to solve Anthony and Carmelo's argument we must first look at the rent which they pay and compare them both in order to see which rent would be the best for them between a time period. The rent costs are:

Anthony: \$300 per month plus a \$2100 initial fee

Carmelo: \$600 per month plus no initial fee

After analyzing their situation, it is understood mathematically that the Anthony's rent is a partial variation and Carmelo's is a direct variation which would make it difficult to understand.

This relation shows how the cost changes over time and the best way to visually see this is on a line graph which will show you time frame when Anthony's rent is better than Carmelo's and when Carmelo's rent is better than Anthony's and also the break-even point or on the graph the point of intersection.

## Equations

m=number of months c=total cost

Anthony: C=300n+2100

Carmelo: C=600n

## Analyze The Graph

This graph shows the time frame when Carmelo's rent is better than Anthony's and when Anthony's is better.

By looking at this graph, I analyzed it over a 6 month period and Carmelo's rent was better for 4 month. Although, they both finally had a break-even point at the 5th month mark when they had both payed the same amount of rent which was \$3600.

Although, after the break-even point Carmelo ended up paying more money than Anthony and he had to pay \$300 more than Anthony during the 6th month so in the longer run Anthony has a better rent deal.

## Conclusion

So in the end the person who started paying the least rent ended up paying the most. These two plan on living in the area which they rent for about a year and if we were to extrapolate the data Carmelo would end up paying \$1600 more dollars than Anthony so in conclusion Carmelo should switch over to Anthony's rent deal as soon as possible to save himself money.